SOLUTION: What payment made at the end of each year for 18 years will amount to $16 OOO at 4.2% compounded monthly?

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Question 1207416: What payment made at the end of each year for 18 years will amount to $16 OOO at 4.2% compounded monthly?
Answer by ikleyn(52864) About Me  (Show Source):
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What payment made at the end of each year for 18 years will amount to $16,OOO at 4.2% compounded monthly?
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As it is given in the post, this annuity is not standard: the payments are made at the end of each year,
while compounding is made at the end of each month.


Analytic formulas exist only for coinciding schedules of payments and compounding.


But we can use an equivalent standard synchronized scheme, considering payments at the end of each year 
and compounding at the end of each year with the highlight%28highlight%28effective%29%29  annual multiplicative growth rate  

    1+r = %281%2B0.042%2F12%29%5E12 = 1.042818007.    (1)


Now we can use a standard formula for such ordinary annuity 

    FV = P%2A%28%28%281%2Br%29%5E18-1%29%2Fr%29.    (2)


In this formula, FV is the future value in 18 years; P is the annual payment, the unknown value
which we should find.


We calculate the factor in the formula (2) separately

    %28%281%2Br%29%5E18-1%29%2Fr = %28%281.042818007%29%5E18-1%29%2F0.042818007 = 26.31908947.


Then from formula (2) we find

    P = FV%2F26.31908947 = 16000%2F26.31908947 = 607.93 dollars.


Thus we found out the annual payment value. It is $607.93.    ANSWER

Solved.